Trying to be constructive OP, and you obviously have more documentation than the summary you were able to provide here, but it looks like the individuals involved on the BA side have not appreciated that the sectors you flew were not the originally ticked ones. The three bullet points make sense if they think you are claiming for HND-ITM which was on 17/11 and operated by JAL. Often when people think they understand a scenario but have grasped the wrong end of the stick it can difficult to dislodge that understanding (and to be fair how many customers actually do know what they are talking about), particularly in a (no doubt) time-poor working environment processing emails involving endless dates, flight codes, and airports. I'd suggest misunderstanding (based on this thread) as the cause, with your follow-up attempts to illuminate the situation not getting through (notice it did take a while even for the tuned minds on this board to fully understand your scenario).